Comparative genomics has revealed a class of non-protein-coding genomic sequences that display an extraordinary degree of conservation between two or more organisms, regularly exceeding that found within protein-coding exons. These elements, collectively referred to as conserved non-coding elements (CNEs), are non-randomly distributed across chromosomes and tend to cluster in the vicinity of genes with regulatory roles in multicellular development and differentiation. CNEs are organized into functional ensembles called genomic regulatory blocks-dense clusters of elements that collectively coordinate the expression of shared target genes, and whose span in many cases coincides with topologically associated domains. CNEs display sequence properties that set them apart from other sequences under constraint, and have recently been proposed as useful markers for the reconstruction of the evolutionary history of organisms. Disruption of several of these elements is known to contribute to diseases linked with development, and cancer. The emergence, evolutionary dynamics and functions of CNEs still remain poorly understood, and new approaches are required to enable comprehensive CNE identification and characterization. Here, we review current knowledge and identify challenges that need to be tackled to resolve the impasse in understanding extreme non-coding conservation.